Pith Number

pith:4S3BQGM2

pith:2011:4S3BQGM2S4GI2LG7627B572EMR

not attested not anchored not stored refs pending

3-manifolds with nonnegative Ricci curvature

Gang Liu

arxiv:1108.1888 v2 · 2011-08-09 · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4S3BQGM2S4GI2LG7627B572EMR}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T03:44:02.807400Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4b618199a970c8d2cdff6be1eff4464792e0e2aea97db4c088ec9688db7a91c

Aliases

arxiv: 1108.1888 · arxiv_version: 1108.1888v2 · doi: 10.48550/arxiv.1108.1888 · pith_short_12: 4S3BQGM2S4GI · pith_short_16: 4S3BQGM2S4GI2LG7 · pith_short_8: 4S3BQGM2

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4S3BQGM2S4GI2LG7627B572EMR \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: e4b618199a970c8d2cdff6be1eff4464792e0e2aea97db4c088ec9688db7a91c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "067b1e6f9635e1cb5cc85d9bdb5ab53378c0de400e7b00e0a1b59fb7ac6dff19",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-08-09T09:15:45Z",
    "title_canon_sha256": "a39fd89c18b444deca98db628fda1850efb88a22240b11f12b00dac4254edb76"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.1888",
    "kind": "arxiv",
    "version": 2
  }
}